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We have definitions for both a square and a circle. By definition, I understand that it's impossible to have a square circle. However, why does the word 'square' have to necessarily mean 'a plane figure with four equal sides'? Conceivably, the word square could have been defined as a 'round plane'? Thus making 'a square circle is metaphysically impossible' false?

I'm new to philosophy. So if this question is pathetic I apologize.

Kiprman
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    Welcome to Philosophy SE! It's a good question! Quine notwithstanding, the meaning of the words, or what they describe is what matters and what can be said to be possible or impossible, not the words themselves. Once the meaning is fixed, some things may become impossible. For example, married bachelors are impossible because "bachelor" means unmarried man. You could define bachelor to mean something other than the "standard" definition, but you wouldn't be showing that married bachelors are possible, you'd just be showing that married s are possible. – Adam Sharpe Apr 05 '19 at 21:00
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    I wish philosophers would choose a different example. The unit circle is a square in the taxicab metric. https://en.wikipedia.org/wiki/Taxicab_geometry. What the saying means is that a definition is a definition. You can't have a married bachelor because a bachelor is unmarried by definition. But you can have a square circle! – user4894 Apr 05 '19 at 21:15
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    The word "square" is a string of letters, it can mean whatever people agree it to mean. So it is vacuous to ask what is "metaphysically possible" for a string of letters to mean. Anything. Therefore, when people talk about metaphysical possibility they do not refer to strings of letters, but to the senses currently attached to them, see SEP on Metaphysical Possibility. – Conifold Apr 05 '19 at 21:18
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    @user4894 Very neat. But I'd argue that "everyday" geometry is implicitly Euclidean, and so we should give the "square circle" example a charitable interpretation. I think it's like someone saying 1+1=10 is impossible, and you objecting that it's a bad example because 1+1=10, in base 2. The everyday reading of numbers is base 10, and that is how they meant to be implicitly understood. – Adam Sharpe Apr 05 '19 at 22:01
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    Although it is pretty nearly universally accepted that a square circle is metaphysically impossible, there doesn't seem to be any agreement that I can find as to why. I suspect a lot of people will point out that we can deduce a logical contradiction from the definitions/axioms in Euclidean geometry, but then we're introducing additional terms/symbolism so that the "square circle" itself doesn't strictly entail a logical contradiction. For my own part, I'd simply say I have no way to make sense of a square circle, and I intuit from this its metaphysical impossibility. But that's me : ) – Ben W Apr 05 '19 at 23:18
  • A square is just a bad approximation of a circle. Add a side to a square (pentagon) and you get a better approximation. Keep doing that, and eventually.you'll get a circle (at planck length sides) – Richard Apr 06 '19 at 01:03
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    If you cannot understand the problem then just try drawing a square circle. Usually 'metaphysically impossible' means 'contrary to reason and logic'. . . –  Apr 06 '19 at 11:26
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    We can define whatever we want: having done this, we have to consistently use our definitions. This is logic... – Mauro ALLEGRANZA Apr 06 '19 at 16:15
  • metaphysics doesn't seem to be how we can conceivably define words, but how we can conceive of things, guided by argument and language. i'm not a mathematician, but a four sided shape is not a one sided shape. anyway, this seems to me to show the vacuity of confusion about e.g. spinoza's definitions (a recent question). even before Saussure it seems unlikely (to relatively simple me) that anyone could have objected to his definitions merely on the grounds that they could be better expressed as different terms. if not, the translation of philosophical literature would raise huge problems imho –  Apr 07 '19 at 03:54
  • If you say that all squares have 4 corners and all circles have zero corners, then if a square circle exists it must have (presumably) all the properties of a square and of a circle. But to have both 4 corners and 0 corners entails a contradiction. – K9Lucario Apr 09 '19 at 20:47
  • In some sense, OP has reinvented geometric topology :) . Pointing out the linguistic and logical issue does not absorbe the innocence of his question, I imagine the first mathematiciens to have delved into topology had a similar sense of "non-contradiction". Not to disqualify all the comments here, but this question is a philosophical moment, because OP could not just resolve to see why the definitions entail the differences, if he might have pushed - say a few hundred years - he might have reinvented a branch of mathematics. Bachelard would be so proud ! – Gloserio Jun 12 '19 at 15:42
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    Actually, it's philosophy 101: words are only arbitrarily related to the ideas they represent, and we should discuss of ideas rather than words. – armand Oct 22 '21 at 08:58
  • @logikal See the comment of user4894 , second top comment ;) – Amr Oct 22 '21 at 15:06
  • A standard answer to questions of this sort is "If my grandmother had wheels she would have been a bicycle." The point being that it is not particularly interesting to ask what different conclusion one might come to if the words in a question meant something other than what they mean. – Daniel Asimov Oct 23 '21 at 02:36

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It depends complety in what definition of square and circle, do you use. If you use the standard definition of square (|x| + |y| = c) and the standard definition of circle (x^1 + y^2 = k), then it is a logical contradiction, therefore it methaphysicaly cannot exists. But if you as a example define square as any geometric shape and use the standard definition of circle, then it can exists.

Erdel von Mises
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  • As soon as you generalize the definition of the circle to ‖(x,y)‖ = k (that is, a circle is the set of all points for which the norm of the vector (x,y) is k), the square and the diamond are in fact special cases of the circle: You get the diamond if ‖(x,y)‖ denotes the 1-norm, the usual circle if it denotes the 2-norm, and the square if it denotes the infinity norm. – Uwe Oct 22 '21 at 10:22
  • @Uwe You can't call circle to all these things. – Erdel von Mises Oct 22 '21 at 10:49
  • Of course I can: "Definition 3.1: Let k be a positive real number, let ‖_‖ be a norm. We call the set { (x,y) | ‖(x,y)‖ = k } a circle with diameter k." – Uwe Oct 22 '21 at 13:25
  • @Uwe generalized circle* – Erdel von Mises Oct 22 '21 at 20:41
  • Have a look at user4894's comment above on the taxicab geometry. – Uwe Oct 22 '21 at 22:30
  • @Uwe I know about that these metrics, I just no agree that you can properly call these things circles. – Erdel von Mises Oct 23 '21 at 00:31